U.S. patent number 9,300,400 [Application Number 13/731,738] was granted by the patent office on 2016-03-29 for communication through multiplexed one-dimensional optical signals.
This patent grant is currently assigned to Alcatel Lucent. The grantee listed for this patent is Andrew R Chraplyvy, Xiang Liu, Chandrasekhar Sethumadhavan, Robert W Tkach, Peter J Winzer. Invention is credited to Andrew R Chraplyvy, Xiang Liu, Chandrasekhar Sethumadhavan, Robert W Tkach, Peter J Winzer.
United States Patent |
9,300,400 |
Liu , et al. |
March 29, 2016 |
Communication through multiplexed one-dimensional optical
signals
Abstract
An example apparatus comprises an optical transmitter which
includes a first processor and at least two optical modulators. The
first processor is configured to generate a first electronic
representation for each of at least two optical signals for
carrying payload data modulated according to a one-dimensional
(1-D) modulation format, and to induce on respective ones of the
first electronic representations an amount of dispersion that
depends on a power-weighted accumulated dispersion (AD.sub.PW) of a
transmission link through which the at least two optical signals
are to be transmitted thereby generating complex-valued electronic
representations of pre-dispersion-compensated optical signals. Each
of the at least two optical modulators modulate a respective analog
version corresponding to a respective one of the complex-valued
electronic representations onto a polarization of an optical
carrier.
Inventors: |
Liu; Xiang (Marlboro, NJ),
Winzer; Peter J (Aberdeen, NJ), Chraplyvy; Andrew R
(Matawan, NJ), Tkach; Robert W (Little Silver, NJ),
Sethumadhavan; Chandrasekhar (Matawan, NJ) |
Applicant: |
Name |
City |
State |
Country |
Type |
Liu; Xiang
Winzer; Peter J
Chraplyvy; Andrew R
Tkach; Robert W
Sethumadhavan; Chandrasekhar |
Marlboro
Aberdeen
Matawan
Little Silver
Matawan |
NJ
NJ
NJ
NJ
NJ |
US
US
US
US
US |
|
|
Assignee: |
Alcatel Lucent
(Boulogne-Billancourt, FR)
|
Family
ID: |
48466976 |
Appl.
No.: |
13/731,738 |
Filed: |
December 31, 2012 |
Prior Publication Data
|
|
|
|
Document
Identifier |
Publication Date |
|
US 20130136449 A1 |
May 30, 2013 |
|
Related U.S. Patent Documents
|
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
|
13601236 |
Aug 31, 2012 |
|
|
|
|
13411462 |
Mar 2, 2012 |
|
|
|
|
13245160 |
Sep 26, 2011 |
8824501 |
|
|
|
61535548 |
Sep 16, 2011 |
|
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H04B
10/25137 (20130101); H04B 10/516 (20130101); H04B
10/5053 (20130101); H04B 10/2507 (20130101) |
Current International
Class: |
H04B
10/2507 (20130101); H04B 10/516 (20130101); H04B
10/2513 (20130101); H04B 10/50 (20130101) |
Field of
Search: |
;398/183-198,147,159,81 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
|
|
|
|
|
|
|
1191726 |
|
Mar 2002 |
|
EP |
|
1341322 |
|
Sep 2003 |
|
EP |
|
WO 2010/137113 |
|
Feb 2010 |
|
WO |
|
2010107439 |
|
Sep 2010 |
|
WO |
|
2010/137113 |
|
Dec 2010 |
|
WO |
|
Other References
Pan Z et al: "Intrabit Polarization Diversity Modulation for the
Mitigation of PMD Effects" IEEE Photonics Technology Letters, IEEE
Service Center, Piscataway, NJ. US, vol. 14 No. 10, Oct. 1, 2002,
pp. 1466-1468, XP011432458. cited by applicant .
International Search Report--PCT/US2012/054755--Filing Date : Sep.
12, 2012, Mailing Date: Nov. 23, 2012--4 pages. cited by applicant
.
Eado Meron et al: "Use of Space Time Coding in Coherent
Polarization-Multiplexed Systems Suffering From
Polarization-Dependent Loss", Optics Letters, OSA, Optical Society
of America, Washington, DC, US, vol. 35, No. 21, Nov. 2, 2010, pp.
3547-3549, XP001558183. cited by applicant .
Gupta S et al: "Dispersion Penalty Mitigation Using Polarization
Mode Multiplexing in Phase Diverse Analog Optical Links". Optical
Fiber Communication/National Fiber Optic Engineers Conference,
2008, OFC/NFOEC 2008, Conference on, IEEE, Piscataway, NJ, USA,
Feb. 24, 2008, pp. 1-3, XP031391214. cited by applicant .
International Search Report--PCT/US2012/054813--Filing Date: Sep.
12, 2012, Mailing Date: Nov. 23, 2012--4 pages. cited by applicant
.
Chongjin Xie et al: "Electronic Nonlinearity Compensation in
112-Gb/s PDM-QPSK Optical Coherent Transmission Systems", 36th
European Conference and Exhibition on Optical Communication ; (ECOC
2010); Torino, Italy, Sep. 19-23, 2010, IEEE, Piscataway, NJ, USA,
Sep. 19, 2010, p. 103, XP031789766. cited by applicant .
International Search Report--PCT/US2012/055012--Filing Date: Sep.
13, 2012, Mailing Date: Dec. 5, 2012--4 pages. cited by
applicant.
|
Primary Examiner: Sedighian; M. R.
Attorney, Agent or Firm: Ralston; Andrew R.
Parent Case Text
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation-in-part of U.S. patent
application Ser. No. 13/601,236 filed Aug. 31, 2012, which is
continuation-in-part of U.S. patent application Ser. No.
13/411,462, filed Mar. 2, 2012, which is a continuation-in-part of
U.S. patent application Ser. No. 13/245,160, filed Sep. 26, 2011,
which claims the benefit of U.S. Provisional Patent Application No.
61/535,548, filed Sep. 16, 2011, both of which are incorporated
herein by reference in their entirety.
Claims
What is claimed is:
1. An apparatus comprising an optical transmitter, the optical
transmitter comprising: a first processor configured to generate a
first electronic representation for each of at least two optical
signals for carrying payload data modulated according to a
one-dimensional (1-D) modulation format, the first processor
further configured to induce on respective ones of the first
electronic representations an amount of dispersion that depends on
a power-weighted accumulated dispersion (AD.sub.pw) of a
transmission link comprising multiple optically amplified
homogenous fiber spans through which the at least two optical
signals are to be transmitted thereby generating complex-valued
electronic representations of pre-dispersion-compensated optical
signals; and at least two optical modulators, each of the at least
two optical modulators for modulating a respective analog version
corresponding to a respective one of the complex-valued electronic
representations onto a polarization of an optical carrier; wherein
the first processor is further configured to generate the
respective ones of the first electronic representations by
performing a unitary transformation on corresponding electronic
representations of two phase-conjugated optical signals that are
modulated according to a two-dimensional (2-D) modulation
format.
2. The apparatus of claim 1 wherein the 1-D modulation format is
Binary Phase Shift Keying (BPSK) or m-ary Pulse Amplitude
Modulation (m-PAM).
3. The apparatus of claim 1 wherein the 2-D modulation format is a
complex valued modulation, quadrature phase-shift keying (QPSK), or
n-constellation-point quadrature-amplitude modulation (n-QAM).
4. The apparatus of claim 1 wherein the unitary transformation has
a generic form of .times. ##EQU00015##
5. The apparatus of claim 1 wherein the first processor is
configured to generate the first electronic representations for two
optical signals for carrying payload data modulated according to a
one-dimensional (1-D) modulation format; and wherein each of the
first electronic representations is generated by performing a
unitary transformation on corresponding electronic representations
of two phase-conjugated optical signals that are modulated
according to a two-dimensional (2-D) modulation format.
6. The apparatus of claim 1 wherein the at least two modulators are
IQ modulators for modulating the complex-valued electronic
representations of the pre-dispersion compensated optical
signals.
7. The apparatus of claim 1 further including at least two
Digital-to-Analog Converters (DACs) for converting respective real
and imaginary parts of one of the complex-valued electronic
representations to analog representations prior to modulation.
8. The apparatus of claim 1 wherein the processor is configured to
generate the first electronic representations by convolving an
E-field representation with a pre-dispersion-compensation
function.
9. The apparatus of claim 1 wherein the at least two optical
signals outputted from the at least two optical modulators are
multiplexed via polarization-division multiplexing (PDM),
wavelength-division multiplexing (WDM), or space-division
multiplexing (SDM), before the at least two optical signals are
transmitted through a transmission link.
10. The apparatus of claim 1 wherein the amount of dispersion
induced on the first electronic representations at least depends on
a power-weighted accumulated dispersion of the transmission link
through which the at least two optical signals are to be
transmitted.
11. The apparatus of claim 1 wherein the first processor is
configured use the overlap-and-add method to electronically
pre-compensate complex fields representing the at least two optical
signals modulated according to a one-dimensional (1-D) modulation
format.
12. The apparatus of claim 1 wherein the apparatus comprises two
optical modulators configured to generate two
orthogonally-polarized pre-dispersion-compensated optical signals
at a same wavelength.
13. The apparatus of claim 1 further comprising: an optical
receiver for receiving versions of at least two
pre-dispersion-compensated optical signals that are originally
modulated according to a 1-D modulation format.
14. The apparatus of claim 13 wherein the optical receiver
comprises: a front-end circuit configured to convert the
polarization components of the received versions of at least two
pre-dispersion-compensated optical signals carrying modulated
payload data into a corresponding plurality of digital electrical
signals; and a second processor configured to: process complex
values representing the received versions to obtain electronic
representations of transmitted 1-D signals; determine payload data
based on the electronic representations of the transmitted 1-D
signals.
15. The apparatus of claim 14 wherein the second processor is
configured to process the complex values representing the received
versions to obtain the electronic representations of the
transmitted 1-D signals is configured to perform one or more of
post-dispersion compensation, time synchronization, channel
estimation, channel compensation, frequency estimation, frequency
compensation, carrier phase estimation, carrier phase compensation,
and forward error correction.
16. The apparatus of claim 14 wherein the second processor is
further configured to perform an inverse transform corresponding to
a unitary transform on ones of the electronic representations of
the transmitted 1-D signals to obtain two phase-conjugated 2-D
signals; and perform coherent superposition of the two
phase-conjugated 2-D signals.
17. The apparatus of claim 16 wherein the inverse transformation
has a generic form of .times. ##EQU00016##
18. A method comprising: generating, by a first processor, a
digital electronic representation for each of at least two optical
signals for carrying payload data modulated according to a
one-dimensional (1-D) modulation format; modulating said at least
two optical signals by ones of at least two optical modulators,
with respective analog versions of said electronic representations,
each analog version corresponding to a respective one of the
digital electronic representations and having induced thereon an
amount of dispersion that depends on a power-weighted accumulated
dispersion (AD) of a transmission link comprising multiple
optically amplified homogenous fiber spans through which the at
least two optical signals are to be transmitted; and further
comprising generating respective ones of the first electronic
representations by performing a unitary transformation on a
corresponding electronic representation of ones of at least two
phase-conjugated optical signals modulated according to a
two-dimensional (2-D) modulation format.
19. The method of claim 18 wherein generating the first electronic
representations comprises: performing pre-dispersion-compensation
to induce an amount of dispersion on the first electronic
representation for each of at least two optical signals in the time
domain.
20. The method of claim 18 wherein generating the first electronic
representations comprises: performing the
pre-dispersion-compensation to induce an amount of dispersion on
the first electronic representation for each of at least two
optical signals in the frequency domain.
21. The method of claim 18 wherein the amount of dispersion induced
on the at least two optical signals is about--AD.sub.pw/2, where
AD.sub.pw is the power-weighted accumulated dispersion of the
transmission link through which the two optical signals are to be
transmitted.
22. The method of claim 18 wherein the at least two optical signals
outputted from the at least two optical modulators are multiplexed
via polarization-division multiplexing (PDM), wavelength-division
multiplexing (WDM), or space-division multiplexing (SDM), before
the signals are transmitted through a transmission link.
23. The method of claim 18 wherein the at least two optical signals
are received by an optical receiver for recovering the payload
data.
Description
FIELD
The invention(s) relate to optical communication equipment and,
more specifically but not exclusively, to equipment for managing
data transport through a nonlinear and/or noisy optical
channel.
DESCRIPTION OF THE RELATED ART
This section introduces aspects that may help facilitate a better
understanding of the invention(s). Accordingly, the statements of
this section are to be read in this light and are not to be
understood as admissions about what is in the prior art or what is
not in the prior art.
Forward error correction (FEC) uses systematically generated
redundant data to reduce the bit-error rate (BER) at the receiver.
The cost of this reduction is a concomitant increase in the
required forward-channel bandwidth, the latter being dependent on
the overhead of the FEC code. In general, an FEC code with a larger
overhead or lower net data rate is used for a noisier channel. When
the channel conditions change over time, the net data rate and/or
the FEC code can be adaptively changed to maintain an acceptable
BER. However, one problem with FEC coding, as applied to optical
transmission systems, is that the coding-gain differences among
various implementable FEC codes usually do not exceed a certain
maximum value, as given by Shannon's information capacity theory.
In long-haul optical fiber transmission, fiber nonlinear effects
further limit the transmission performance. In addition, the
digital signal processing (DSP) complexity for capacity-approaching
FEC codes can be forbiddingly high. Therefore, for certain optical
fiber channels, additional and/or alternative
performance-enhancement techniques may be needed to improve the
transmission performance.
SUMMARY
The following presents a simplified summary of the disclosed
subject matter in order to provide a basic understanding of some
aspects of the disclosed subject matter. This summary is not an
exhaustive overview of the disclosed subject matter. It is not
intended to identify key or critical elements of the disclosed
subject matter or to delineate the scope of the disclosed subject
matter. Its sole purpose is to present some concepts in a
simplified form as a prelude to the more detailed description that
is discussed later.
Methods for increasing nonlinear transmission performance without
changing the transmission link include (1) using digital nonlinear
compensation; and (2) using phase conjugated twin waves (PCTW) as
described in U.S. patent application Ser. No. 13/601326, filed Aug.
31, 2012, incorporated herein by reference. Digital nonlinear
compensation usually requires high digital signal processing (DSP)
complexity, especially for dispersion-unmanaged optical fiber
transmission where a large number of nonlinear compensation steps
are required. In addition, digital nonlinear compensation usually
only provides mitigation of intra-channel nonlinear impairments,
and offers a modest improvement in nonlinear transmission
performance in typical wavelength-division multiplexed transmission
systems. PCTW provides improvement in the quality of an optical
signal after transmission by performing digital constructive
summation of a set of two or more optical variants. Optical
variants are correlated optical signals which carry the same piece
of payload data, bit-word, or bit sequence but differ from each
other in at least one of their degrees of freedom, e.g., in one or
more of the time of transmission, spatial localization,
polarization of light, optical carrier wavelength and subcarrier
frequency. The constructive summation tends to average out, to a
certain degree, the deleterious effects of both linear and
nonlinear noise/distortions imparted on the individual optical
variants in the optical transmission link because said
noise/distortions are incoherent in nature. The optical variants
can be the same as the original optical signal intended for
transmission, or phase-scrambled copies of the original signal.
Nonlinear distortions imparted on two phase-conjugated signals
during transmission can be essentially opposite to each other (or
anti-correlated) when the phase conjugation is removed at the
receiver. Therefore, when two phase-conjugated optical variants
carrying the same modulated payload symbols are coherently summed
after removing the phase conjugation between them, the nonlinear
distortions imparted on the two phase-conjugated optical variants
would essentially cancel. It is further found that in highly
dispersive transmission, application of a symmetric dispersion map
may be additionally utilized in order to achieve a more effective
cancellation of the nonlinear distortions imparted on the two
phase-conjugated optical variants. The symmetric dispersion map can
be realized by pre-compensating the phase-conjugated optical
variants by an amount of dispersion that depends on the accumulated
dispersion (e.g., power-weighted accumulated dispersion
(AD.sub.PW)) of a transmission link, through which the optical
variants are to be transmitted. This methodology effectively
improves signal quality after nonlinear dispersive transmission,
beyond what can be achieved by coherently summing two optical
variants that are either duplicated or phase-scrambled copies of a
same optical signal.
It has been recently found that Polarization-Division-Multiplexed
Binary-Phase-Shift-Keying (PDM-BPSK) offers <.about.3 dB
improvement (in signal Q factor) as compared to PDM
Quadrature-Phase-Shift-Keying (PDM-QPS)K (for the same moduation
symbol rate) in dispersion-uncompensated transmission links. PCTW
have been found to offer >5.5 dB improvement over PDM-QPSK
(again for the same modulation symbol rate). However, the
implementation of PCTW requires an accurate phase alignment between
the twin waves.
Accordingly, provided herein are methodologies in which (1) a pair
of multiplexed 1-Dimensional signals (M-1DS) are generated, which
may be generated by performing an unitary transform on a PCTW; (2)
a pre-determined amount of dispersion is added on the components of
the M-1DS, such that the power-weighted dispersion distribution
(PWDD) function of the transmission link is centered near zero; (3)
the pre-dispersion-compensated M-1DS (PreC-M-1DS) are transmitted
over an optical transmission link; (4) and coherently detected at
an optical receiver; and (5) the data carried by the M-1D is
recovered. The M-1DS can be multiplexed via polarization-division
multiplexing (PDM), wavelength-division multiplexing (WDM), or
space-division multiplexing (SDM), before the signals are
transmitted through the transmission link. Embodiments according to
the principles described result in the fiber nonlinear penalty
being substantially reduced. When the M-1DS are multiplexed through
PDM, the nonlinear distortions (or noises) of these two
polarization components of the M-1D are "squeezed" along the
direction that is orthogonal to the decision line of the 1-D
signal, and would not cause decision errors. The described
modulation scheme using PMD is referred to herein as "optimally
pre-compensated PDM 1-D modulation" (PreC-PDM-1D). Common 1-D
modulation formats include binary phase-shift keying (BPSK) and
m-ary pulse-amplitude modulation (m-PAM).
One example apparatus comprises an optical transmitter which
includes a first processor and at least two optical modulators. The
first processor is configured to generate a first electronic
representation for each of at least two optical signals for
carrying payload data modulated according to a one-dimensional
(1-D) modulation format, and to induce on respective ones of the
first electronic representations an amount of dispersion that
depends on a power-weighted accumulated dispersion (AD.sub.PW) of a
transmission link through which the at least two optical signals
are to be transmitted thereby generating complex-valued electronic
representations of pre-dispersion-compensated optical signals. Each
of the at least two optical modulators modulate a respective analog
version corresponding to a respective one of the complex-valued
electronic representations onto a polarization of an optical
carrier.
In one embodiment, the 1-D modulation format is Binary Phase Shift
Keying (BPSK) or m-ary Pulse Amplitude Modulation (m-PAM).
In one embodiment, the first processor is further configured to
generate the respective ones of the first electronic
representations by performing a unitary transformation on
corresponding electronic representations of two phase-conjugated
optical signals that are modulated according to a two-dimensional
(2-D) modulation format. The unitary transformation may have a
generic form of
.times. ##EQU00001##
In one embodiment, the 2-D modulation format is a complex valued
modulation, quadrature phase-shift keying (QPSK), or
n-constellation-point quadrature-amplitude modulation (n-QAM).
In one embodiment, the first processor is configured to generate
the first electronic representations for two optical signals for
carrying payload data modulated according to a one-dimensional
(1-D) modulation format; and wherein each of the first electronic
representations is generated by performing a unitary transformation
on corresponding electronic representations of two phase-conjugated
optical signals that are modulated according to a two-dimensional
(2-D) modulation format.
In one embodiment, the at least two modulators are IQ modulators
for modulating the complex-valued electronic representations of the
pre-dispersion compensated optical signals.
In one embodiment, the transmitter also includes at least two
Digital-to-Analog Converters (DACs) for converting respective real
and imaginary parts of one of the complex-valued electronic
representations to analog representations prior to modulation.
In one embodiment, the processor is configured to generate the
first electronic representations by convolving an E-field
representation with a pre-dispersion-compensation function.
In one embodiment, the at least two optical signals outputted from
the at least two optical modulators are multiplexed via
polarization-division multiplexing (PDM), wavelength-division
multiplexing (WDM), or space-division multiplexing (SDM), before
the at least two optical signals are transmitted through a
transmission link.
In one embodiment, the amount of dispersion induced on the first
electronic representations at least depends on a power-weighted
accumulated dispersion of the transmission link through which the
at least two optical signals are to be transmitted.
In one embodiment, the first processor is configured use the
overlap-and-add method to electronically pre-compensate complex
fields representing the at least two optical signals modulated
according to a one-dimensional (1-D) modulation format.
In one embodiment, the apparatus comprises two optical modulators
configured to generate two orthogonally-polarized
pre-dispersion-compensated optical signals at a same
wavelength.
In one embodiment, the apparatus also includes an optical receiver
for receiving versions of at least two pre-dispersion-compensated
optical signals that are originally modulated according to a 1-D
modulation format.
In one embodiment, the optical receiver includes a front-end
circuit configured to convert the polarization components of the
received versions of at least two pre-dispersion-compensated
optical signals carrying modulated payload data into a
corresponding plurality of digital electrical signals, and a second
processor configured to: process complex values representing the
received versions to obtain electronic representations of
transmitted 1-D signals and determine payload data based on the
electronic representations of the transmitted 1-D signals.
In one embodiment, the second processor is configured to process
the complex values representing the received versions to obtain the
electronic representations of the transmitted 1-D signals is
configured to perform one or more of post-dispersion compensation,
time synchronization, channel estimation, channel compensation,
frequency estimation, frequency compensation, carrier phase
estimation, carrier phase compensation, and forward error
correction.
In one embodiment, the second processor is configured to perform an
inverse transform corresponding to a unitary transform on ones of
the electronic representations of the transmitted 1-D signals to
obtain two phase-conjugated 2-D signals, and perform coherent
superposition of the two phase-conjugated 2-D signals.
In one embodiment, the inverse transformation has a generic form
of
.times. ##EQU00002##
In one example method comprising a first processor generates a
first electronic representation for each of at least two optical
signals for carrying payload data modulated according to a
one-dimensional (1-D) modulation format, and ones of at least two
optical modulators modulate a respective analog versions
corresponding to a respective one of the first electronic
representations having induced thereon an amount of dispersion that
depends on an accumulated dispersion (AD) of a transmission link
through which the at least two optical signals are to be
transmitted.
In one embodiment, generating the first electronic representations
comprises performing pre-dispersion-compensation to induce an
amount of dispersion on the first electronic representation for
each of at least two optical signals in the time domain. In one
embodiment, generating the first electronic representations
comprises performing the pre-dispersion-compensation to induce an
amount of dispersion on the first electronic representation for
each of at least two optical signals in the frequency domain.
In one embodiment, the amount of dispersion induced on the at least
two optical signals is about--AD.sub.PW /2, where AD.sub.PW is the
power-weighted accumulated dispersion of the transmission link
through which the two optical signals are to be transmitted.
In one embodiment, the method includes generating respective ones
of the first electronic representations by performing a unitary
transformation on a corresponding electronic representation of ones
of at least two phase-conjugated optical signals modulated
according to a two-dimensional (2-D) modulation format.
In one embodiment, said generating comprises generating the first
electronic representations of two optical signals for carrying
payload data modulated according to a one-dimensional (1-D)
modulation format, wherein the first electronic representations are
generated by performing a unitary transformation on corresponding
electronic representations of two phase-conjugated optical signals
modulated according to a two-dimensional (2-D) modulation
format.
In one embodiment, the at least two optical signals outputted from
the at least two optical modulators are multiplexed via
polarization-division multiplexing (PDM), wavelength-division
multiplexing (WDM), or space-division multiplexing (SDM), before
the signals are transmitted through a transmission link.
In one embodiment, the at least two optical signals are received by
an optical receiver for recovering the payload data.
BRIEF DESCRIPTION OF THE DRAWINGS
Other aspects, features, and benefits of various embodiments of the
invention will become more fully apparent, by way of example, from
the following detailed description and the accompanying drawings,
in which:
FIG. 1 shows a block diagram of an optical transmission system
according to one embodiment of the invention;
FIG. 2 shows a flowchart of a signal-processing method that can be
implemented in the transmitter of the optical transmission system
shown in FIG. 1 according to one embodiment of the invention;
FIG. 3 shows a flowchart of a signal-processing method that can be
implemented in the receiver of the optical transmission system
shown in FIG. 1 according to one embodiment of the invention;
FIG. 4 shows experimentally measured 15-Gbaud BPSK signal
constellations in the back-to-back configuration (left), after
6,400 km (80.times.80 km SSMF spans) with -2 dBm (middle) and 0 dBm
(right) signal launch powers, for the case without pre-dispersion
compensation (upper row) and with the optimal pre-dispersion
compensation (lower row).
FIG. 5 shows simulated 16-QAM signal constellations (left column)
without (upper row) and with (lower row) pre-dispersion
compensation, as compared to recovered 4-PAM signal constellations
(right column) without (upper row) and with (lower row)
pre-dispersion compensation.
While the disclosed subject matter is susceptible to various
modifications and alternative forms, specific embodiments thereof
have been shown by way of example in the drawings and are herein
described in detail. It should be understood, however, that the
description herein of specific embodiments is not intended to limit
the disclosed subject matter to the particular forms disclosed, but
on the contrary, the intention is to cover all modifications,
equivalents, and alternatives falling within the scope of the
appended claims.
DETAILED DESCRIPTION
Illustrative embodiments are described below. In the interest of
clarity, not all features of an actual implementation are described
in this specification. It will of course be appreciated that in the
development of any such actual embodiment, numerous
implementation-specific decisions should be made to achieve the
developers' specific goals, such as compliance with system-related
and business-related constraints, which will vary from one
implementation to another. Moreover, it will be appreciated that
such a development effort might be complex and time-consuming, but
would nevertheless be a routine undertaking for those of ordinary
skill in the art having the benefit of this disclosure. The
description and drawings merely illustrate the principles of the
claimed subject matter. It should thus be appreciated that those
skilled in the art may be able to devise various arrangements that,
although not explicitly described or shown herein, embody the
principles described herein and may be included within the scope of
the claimed subject matter. Furthermore, all examples recited
herein are principally intended to be for pedagogical purposes to
aid the reader in understanding the principles of the claimed
subject matter and the concepts contributed by the inventor(s) to
furthering the art, and are to be construed as being without
limitation to such specifically recited examples and
conditions.
The disclosed subject matter is described with reference to the
attached figures. Various structures, systems and devices are
schematically depicted in the drawings for purposes of explanation
only and so as to not obscure the description with details that are
well known to those skilled in the art. Nevertheless, the attached
drawings are included to describe and explain illustrative examples
of the disclosed subject matter. The words and phrases used herein
should be understood and interpreted to have a meaning consistent
with the understanding of those words and phrases by those skilled
in the relevant art. No special definition of a term or phrase,
i.e., a definition that is different from the ordinary and
customary meaning as understood by those skilled in the art, is
intended to be implied by consistent usage of the term or phrase
herein. To the extent that a term or phrase is intended to have a
special meaning, i.e., a meaning other than that understood by
skilled artisans, such a special definition is expressly set forth
in the specification in a definitional manner that directly and
unequivocally provides the special definition for the term or
phrase. Additionally, the term, "or," as used herein, refers to a
non-exclusive "or," unless otherwise indicated (e.g., "or else" or
"or in the alternative"). Also, the various embodiments described
herein are not necessarily mutually exclusive, as some embodiments
can be combined with one or more other embodiments to form new
embodiments.
FIG. 1 shows a block diagram of an optical transmission system 100
according to one embodiment of the invention. System 100 has an
optical transmitter 110 that is configured to transmit a pair of
multiplexed 1-D optical signals (M-1DS) through
polarization-division multiplexing (PDM). System 100 also has an
optical receiver 190 that is configured to process the received
optical signals to recover the corresponding original data in a
manner that reduces the BER compared to the BER attainable without
use of embodiments of the invention. Transmitter 110 and receiver
190 are connected to one another via an optical transmission link
140.
Transmitter 110 receives an input stream 102 of payload data and
applies it to a digital signal processor (DSP) 112. Processor 112
processes input stream 102 to generate digital signals
114.sub.1-114.sub.4. In each signaling interval (time slot),
signals 114.sub.1 and 114.sub.2 carry digital values that represent
the in-phase (I) component and quadrature (Q) component,
respectively, of a corresponding constellation symbol intended for
transmission using X-polarized light. Signals 114.sub.3 and
114.sub.4 similarly carry digital values that represent the I and Q
components, respectively, of the corresponding constellation symbol
intended for transmission using Y-polarized light. Digital signals
114.sub.1-114.sub.4 are also pre-dispersion-compensated by an
amount of dispersion that depends on the power-weighted accumulated
dispersion (AD.sub.PW) of a transmission link through which the two
optical signals are to be transmitted. When the signal power
evolution of a given span of the fiber link is unknown, a nominal
average power that is dependent on the signal launch power into
this span can be assumed for this span. Given a typical fiber loss
coefficient of 0.2 dB/km, and a typical fiber span length of 100
km, the nominal average power is about 5 times less than the signal
launch power. Note that although each 1-D signal can be represented
by a real-valued waveform, complex-valued waveform (having both I
and Q components) is needed to represent the 1-D signal after
pre-dispersion compensation.
An electrical-to-optical (E/O) converter (also sometimes referred
to as a front end) 116 of transmitter 110 transforms digital
signals 114.sub.1-114.sub.4 into a modulated optical output signal
130. More specifically, digital-to-analog converters (DACs)
118.sub.1 and 118.sub.2 transform digital signals 114.sub.1 and
114.sub.2 into an analog form to generate drive signals I.sub.X and
Q.sub.X, respectively. Drive signals I.sub.X and Q.sub.X are then
used, in a conventional manner, to drive an I-Q modulator
124.sub.X. Based on drive signals I.sub.X and Q.sub.X, I-Q
modulator 124.sub.X modulates an X-polarized beam 122.sub.X of
light supplied by a laser source 120.sub.X, thereby generating a
modulated optical signal 126.sub.X.
DACs 118.sub.3 and 118.sub.4 similarly transform digital signals
114.sub.3 and 114.sub.4 into an analog form to generate drive
signals I.sub.Y and Q.sub.Y, respectively. Based on drive signals
I.sub.Y and Q.sub.Y, an I-Q modulator 124.sub.Y modulates a
Y-polarized beam 122.sub.Y of light supplied by a laser source
120.sub.Y, thereby generating a modulated optical signal 126.sub.Y.
A polarization beam combiner 128 combines modulated optical signals
126.sub.X and 126.sub.Y to generate optical output signal 130.
The pair of pre-dispersion-compensated 1-D optical signals are
transmitted over an optical transmission link in different
dimensions, e.g., in one or more of the time of transmission,
spatial localization, polarization of light, optical carrier
wavelength, and subcarrier frequency. More details on the use of
different dimensions in transmitting the optical signals can be
found in U.S. patent application Ser. No. 13/601,326, filed Aug.
31, 2012, which is continuation-in-part of U.S. patent application
Ser. No. 13/411,462, filed Mar. 2, 2012, which is a
continuation-in-part of U.S. patent application Ser. No.
13/245,160, filed Sep. 26, 2011.
The processor 112 may also add pilot symbols and/or pilot-symbol
sequences to each of signals 114.sub.1, 114.sub.2, 114.sub.3, and
114.sub.3. One purpose of the added pilot symbols and/or
pilot-symbol sequences is to form an optical frame having a
well-defined structure. This structure can be used at receiver 190
to distinguish the optical symbols corresponding to the payload
data from the pilot symbols/sequences, and to ensure the phase
alignment between the optical variants. The pilot symbols/sequences
can then be used to perform one or more of (i) time
synchronization, (ii) channel estimation and compensation, (iii)
frequency estimation and compensation, and (iv) phase estimation
and compensation. An enabling description of possible frame
structures and suitable pilot symbols/sequences can be found, e.g.,
in commonly owned U.S. patent application Ser. No. 12/964,929
(filed on Dec. 10, 2010), which is incorporated herein by reference
in its entirety.
System 100 has an optical add-drop multiplexer (OADM) configured to
add signal 130, as known in the art, to other optical signals that
are being transported via optical transmission link 140. Link 140
is illustratively shown as being an amplified link having a
plurality of optical amplifiers 144 configured to amplify the
optical signals that are being transported through the link, e.g.,
to counteract signal attenuation. Note that an optical link that
does not have optical amplifiers can alternatively be used as well.
After propagating the intended length of link 140, signal 130 is
dropped from the link via another optical add-drop multiplexer,
OADM 146, and directed to receiver 190 for processing. Note that
the optical signal applied to receiver 190 by OADM 146 is labeled
130', which signifies the fact that, while in transit between
transmitter 110 and receiver 190, signal 130 may accumulate noise
and other signal distortions due to various linear effects and
nonlinear effects in the optical fiber. One type of a fiber
nonlinear effect is intra-channel four-wave mixing (IFWM), which is
a function of the phases and amplitudes of the corresponding
optical symbols. Another type of a fiber nonlinear effect is
inter-channel cross-phase modulation (XPM) caused by neighboring
wavelength-division multiplexed (WDM) channels.
Receiver 190 has a front-end circuit 172 comprising an
optical-to-electrical (O/E) converter 160, four analog-to-digital
converters (ADCs) 166.sub.1-166.sub.4, and an optical local
oscillator (OLO) 156. O/E converter 160 has (i) two input ports
labeled S and R and (ii) four output ports labeled 1 through 4.
Input port S receives optical signal 130'. Input port R receives an
optical reference signal 158 generated by optical local oscillator
156. Reference signal 158 has substantially the same
optical-carrier frequency (wavelength) as signal 130'. Reference
signal 158 can be generated, e.g., using a tunable laser controlled
by a wavelength-control loop (not explicitly shown in FIG. 1) that
forces an output wavelength of the tunable laser to closely track
the carrier wavelength of signal 130'.
O/E converter 160 operates to mix input signal 130' and reference
signal 158 to generate eight mixed optical signals (not explicitly
shown in FIG. 1). O/E converter 160 then converts the eight mixed
optical signals into four electrical signals 162.sub.1-162.sub.4
that are indicative of complex values corresponding to the two
orthogonal-polarization components of signal 130'. For example,
electrical signals 162.sub.1 and 162.sub.2 may be an analog
in-phase signal and an analog quadrature-phase signal,
respectively, corresponding to the X-polarization component of
signal 130'. Electrical signals 162.sub.3 and 162.sub.4 may
similarly be an analog in-phase signal and an analog
quadrature-phase signal, respectively, corresponding to the
Y-polarization component of signal 130'.
In one embodiment, O/E converter 160 is a polarization-diverse
90-degree optical hybrid (PDOH) with four balanced photo-detectors
coupled to its eight output ports. Additional information on
various O/E converters that can be used to implement O/E converter
160 in various embodiments of system 100 are disclosed, e.g., in
U.S. Patent Application Publication Nos. 2010/0158521 and
2011/0038631, and International Patent Application No.
PCT/US09/37746 (filed on Mar. 20, 2009), all of which are
incorporated herein by reference in their entirety.
Each of electrical signals 162.sub.1-162.sub.4 generated by O/E
converter 160 is converted into digital form in a corresponding one
of ADCs 166.sub.1-166.sub.4. Optionally, each of electrical signals
162.sub.1-162.sub.4 may be amplified in a corresponding amplifier
(not explicitly shown) prior to the resulting signal being
converted into digital form. Digital signals 168.sub.1-168.sub.4
produced by ADCs 166.sub.1-166.sub.4 are processed by a digital
signal processor (DSP) 170, e.g., as further described below in
reference to FIG. 3, to recover the data of the original input
stream 102 applied to transmitter 110.
FIG. 2 shows a flowchart of a signal-processing method 200 that can
be employed by processor 112 (FIG. 1) to generate digital signals
114.sub.1-114.sub.4 according to one embodiment of the invention
where pre-dispersion-compensated optical signals modulated
according to a one dimensional (1-D) modulation format are carried
on two orthogonal polarization states of a same wavelength
channel.
At optional step 205 of method 200, payload data 102 are processed
to obtain the payload signal sequence, E.sub.2D(t), using a given
two-dimensional (2-D) modulation format. The 2-D modulation format
used can be selected from the group consisting of complex valued
modulation, quadrature phase-shift keying (QPSK),
n-constellation-point quadrature-amplitude modulation (n-QAM), or
any suitable combination thereof. This step may include the payload
signal sequence E.sub.2D(t), and its phase-conjugated variant
E.sub.2D*(t-.tau.) are respectively assigned to the x-polarization
and y-polarization components of the optical signal to be
modulated
At step 210 of method 200, either payload data 102 are processed to
obtain the a pair of signal sequences, Ex(t) and Ey(t), using a
given one-dimensional (1-D) modulation format. The 1-D modulation
format used can be selected from the group consisting of Binary
Phase Shift Keying (BPSK) or m-ary Pulse Amplitude Modulation
(m-PAM) or any suitable combination thereof. The pair of 1-D
signals can also be obtained by performing a unitary transformation
on two phase-conjugated signals modulated according to a
two-dimensional (2-D) modulation format to carry the payload data.
In one embodiment, the unitary transformation is in the generic
form of
.times. ##EQU00003##
By generic form it is meant that the given generic form can be
further transformed, e.g., multiplied by a complex constant, and
retain the same effect.
At step 220 of method 200, pre-dispersion compensation is applied
to the E-fields of both x- and y-polarization components of the
optical signal to be modulated resulting in complex-valued
E-fields, Ex_pre and Ey_pre respectively. The amount of dispersion
induced by the pre-dispersion compensation depends on AD.sub.PW,
where AD.sub.PW is the power-weighted accumulated dispersion of
optical fiber transmission link 140. As an example, the
power-weighted accumulated dispersion of a transmission link
comprising multiple optically amplified homogenous fiber spans is
defined as:
.times..intg..times.e.function..times..function..times..times.d
##EQU00004## where L is the link distance, and C(z) is accumulated
dispersion at distance z along the transmission link
.function..intg..times..beta..function.'.times.d' ##EQU00005##
where .beta..sub.2(z') is the group-velocity dispersion coefficient
at distance z' along the link.
In the above equation, G(z) is the logarithmic loss/gain evolution
of the optical signal
.function..intg..times..function.'.alpha..function.'.times.d'
##EQU00006## where g(z') and .alpha.(z') are the gain and loss
coefficients at distance z' along the transmission link,
respectively, and L.sub.eff is the effective length of the
transmission link
.intg..times.e.function..times..times.d ##EQU00007##
To generate "pre-dispersion-compensated" optical signals, the
E-fields of the original signals, E.sub.n, Pre(t), are effectively
convolved with a pre-dispersion-compensation function H.sub.Pre(t)
as follows E.sub.n, Pre(t)=H.sub.Pre(t)E.sub.n(t) (5) where ``
denotes convolution as defined:
.function..function..intg..infin..infin..times..function..tau..times..fun-
ction..tau..times..times.d.tau. ##EQU00008##
A convolution is the integral of the product of two functions after
one is reversed and shifted producing a third function that is
typically viewed as a modified version of one of the original
functions, giving the area overlap between the two functions as a
function of the amount that one of the original functions is
translated. The above convolution operation can be simply realized
in the frequency domain as H(t)E(t)=F.sup.-1{F[H(t)]F[E(t)]}, (7)
where F(x) is the Fourier transform of function x. The size of the
discrete Fourier transform (DFT) and inverse DFT (IDFT) used to
covert time-domain signal E-field to the frequency domain and back
can vary between being at least the same size as the
dispersion-induced channel memory length to 10 times such length,
the size being chosen to balance processing latency and hardware
requirements with acceptable accuracy. The size of the DFT and IDFT
used to covert time-domain signal E-field to the frequency domain
and back is usually a few times the dispersion-induced channel
memory length. The frequency-domain dispersion compensation can be
realized by using the overlap-and-add approach. A more detailed
description on the overlap-and-add approach can be found in a paper
entitled "Coherent optical single carrier transmission using
overlap frequency domain equalization for long-haul optical
systems," published in J. Lightwave Technol., 27, 3721-3728 (2009)
by R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y.
Miyamoto, which is incorporated herein by reference in its
entirety.
In one embodiment, the amount of dispersion induced by the
pre-dispersion compensation is preferably about--AD.sub.PW/2, where
AD.sub.PW is the power-weighted accumulated dispersion of optical
fiber transmission link 140. Under this condition, the dispersion
map is made symmetric about zero dispersion (i.e., pre-dispersion
compensation applied such that about half way through the
transmission link, the accumulated dispersion is zero), we have
C(z).apprxeq.-C(L-z), (8) and G(z).apprxeq.G(L -z). (9)
The dimensionless nonlinear transfer function, defined as
.eta..function..xi..times..intg..times.e.function.I.times..times..xi..tim-
es..times..function..times..times.d ##EQU00009## then becomes
essentially a real-valued number, when Eqs. (8) and (9) are
applied, because
.eta..function..xi..times..intg..times.e.function.I.times..times..xi..tim-
es..times..function.e.function.I.times..times..xi..times..times..function.-
.times..times.d.apprxeq..times..intg..times..times..times.e.function..time-
s..function..xi..times..times..function..times..times.d
##EQU00010## This means that, for the case of transmission with the
symmetric dispersion map, we have .eta.(.xi.).apprxeq.(.xi.)*
(12)
Based on a perturbation approach, we can express the nonlinear
distortion on the E-field of an optical signal (E) after the
transmission in the frequency domain as
.delta..times..times..function..omega..times..times..gamma..times..times.-
.times..times..intg..infin..infin..times..times.d.omega..times..intg..infi-
n..infin..times..times.d.omega..times..eta..function..omega..times..omega.-
.times..function..omega..omega..times..function..omega..omega..times..func-
tion..omega..omega..omega. ##EQU00011## where i is the imaginary
unit, * denotes complex conjugate, P.sub.0, .gamma. are
respectively the fiber nonlinear Kerr coefficient and mean average
signal launch power into each fiber span.
In the case of PCTW-based transmission, the phase-conjugated
optical variant E.sub.c(t) is equal to E(t)* before transmission.
In the frequency domain, we have E.sub.c(.omega.)=E(-.omega.)*
using the conjugation property of Fourier transform (e.g., see
http://en.wikipedia.org/wiki/Fourier transform). We can then write
the nonlinear distortion on the E-field of the phase-conjugated
optical variant as
.delta..times..times..function..omega..times..times..times..gamma..times.-
.times..times..times..intg..infin..infin..times..times.d.omega..times..int-
g..infin..infin..times..times.d.omega..times..eta..function..omega..times.-
.omega..times..function..omega..omega..times..function..omega..omega..time-
s..function..omega..omega..omega..times..times..times..gamma..times..times-
..times..times..intg..infin..infin..times..times.d.omega..times..intg..inf-
in..infin..times..times.d.omega..times..eta..function..omega..times..omega-
..times..function..omega..omega..times..function..omega..omega..times..fun-
ction..omega..omega..omega..apprxeq..times..times..times..gamma..times..ti-
mes..times..times..intg..infin..infin..times..times.d.omega..times..intg..-
infin..infin..times..times.d.omega..times..eta..function..omega..times..om-
ega..times..times..omega..omega..times..function..omega..omega..times..fun-
ction..omega..omega..omega..apprxeq..times..delta..times..function..omega.
##EQU00012##
In the derivation of the above equation, we use the fact that
.eta.(.omega..sub.1.omega..sub.2) is essentially real-valued, or
.eta.(.omega..sub.1.omega..sub.2).apprxeq..eta.(.omega..sub.1.omega..sub.-
2)*, based on Eq. (12). The above equation reveals that the
nonlinear distortions experienced by two phase-conjugated optical
variants are opposite to each other or anti-correlated in the time
domain (after their phase conjugation relation is removed), i.e.,
[.delta.E.sub.c(L,t)]*=F{.delta.E.sub.c(L,.omega.)}*.apprxeq.F{-[.delta.E-
(L,-.omega.)]*}*=[-.delta.E(L,t)*]*=-.delta.E(L,t) (15) Where F{ }
denotes the Fourier transform. So, the full cancellation of
nonlinear distortions upon coherent superposition of the received
phase-conjugated optical variants is evident from
E(L,t)+[E.sub.c(L,t)]*=[E(t)+.delta.E(L,t)]+[E*(t)+.delta.E.sub.c(L,t)]*=-
E(t)+.delta.E(L,t)+E(t)+[.delta.E.sub.c(L,t)]*.apprxeq.2E(t)
(16)
In the case of transmission with optical signals modulated
according to a 1-D modulation format, each signal waveform can be
expressed as real-valued, or E(t)=E(t)*, we have
E(.omega.)=E(-.omega.)* (17) Using Eq. (13), we then have
.delta..times..times..function..omega..times..times..times..gamma..times.-
.times..times..times..intg..infin..infin..times..times.d.omega..times..int-
g..infin..infin..times..times.d.omega..times..eta..function..omega..times.-
.omega..times..function..omega..omega..times..function..omega..omega..time-
s..function..omega..omega..omega..times..times..times..gamma..times..times-
..times..times..intg..infin..infin..times..times.d.omega..times..intg..inf-
in..infin..times..times.d.omega..times..eta..function..omega..times..omega-
..times..function..omega..omega..times..function..omega..omega..times..fun-
ction..omega..omega..omega..times..times..times..gamma..times..times..time-
s..times..intg..infin..infin..times..times.d.omega..times..intg..infin..in-
fin..times..times.d.omega..times..eta..function..omega..times..omega..time-
s..function..omega..omega..times..function..omega..omega..times..function.-
.omega..omega..omega..times..delta..times..times..function..omega.
##EQU00013## which means that the nonlinear distortions .delta.E
(L,t) , are purely imaginary. As the original signal E(t) is
real-valued, the nonlinear distortions .delta.E(L,t) are thus
"squeezed" along the direction that is orthogonal to the decision
line (or the nonlinear distortions are "parallel" to the decision
line), and would not cause decision errors (to first order). These
results suggest that in effect, the "nonlinear distortion
cancellation" effect in the case of PCTW is manifested as the
"nonlinear distortion squeezing" effect for 1-D modulation formats
such as BPSK and m-PAM.
It is remarkable that the above cancellation or squeezing of
nonlinear distortions is achieved even in the presence of large
dispersion during fiber transmission (because the nonlinear
distortions at different link locations are different due to the
different accumulated dispersion values at these locations), when
an appropriate amount of dispersion is induced on the
phase-conjugated optical variants at the transmitter side through
pre-dispersion-compensation to make the link dispersion map
symmetric about zero dispersion.
At step 230 of method 200, the digital representations of the real
and imaginary parts of the E-field of the x-polarization component
are converted into analog waveforms by DACs 118.sub.1 and
118.sub.2. At the same time, the digital representations of the
real and imaginary parts of the E-field of the y-polarization
component are converted into analog waveforms by DACs 118.sub.3 and
118.sub.4.
At step 240 of method 200, a pair of
polarization-division-multiplexed I/Q modulators 124.sub.X and
124.sub.Y driven by respective outputs from the DACs 118.sub.1 and
118.sub.2 to generate PDM optical signal 130. While a
two-polarization PDM optical signal is illustrated by this
embodiment, multiple such PDM optical signals may be constructed in
a similar fashion.
FIG. 3 shows a flowchart of a signal-processing method 300 that can
be employed by processor 170 (FIG. 1) to recover data stream 102
from digital signals 168.sub.1-168.sub.4 according to one
embodiment of the invention where pre-dispersion-compensated
optical signals are carried on two orthogonal polarization states
of a same wavelength channel.
At step 310 of method 300, digital signals 168.sub.1-168.sub.4 are
processed to construct two received optical fields corresponding to
two orthogonal polarization components, R.sub.X(t) and
R.sub.y(t).
At step 320 of method 300, post-dispersion compensation is applied
to the E-fields of both x'- and y'-polarization components of the
received optical signal. The amount of dispersion induced by the
post-dispersion compensation is preferably chosen to bring the
overall dispersion experienced by the signal variants to
essentially zero. The post-dispersion compensation can be
implemented in the frequency domain, e.g., by using the
overlap-and-add approach.
At step 330 of method 300, digital signal processing is applied to
achieve time and frequency synchronization. In a representative
implementation, the time-synchronization procedure of step 330
relies on certain properties of pilot-symbol sequences to determine
the start of each optical frame. The known structure of the optical
frame can then be used to identify time slots that have digital
samples and/or digital-signal portions corresponding to the optical
symbols carrying the payload data. The frequency-synchronization
procedure of step 330 may perform electronic estimation and
compensation of a mismatch between the carrier-frequency of input
signal 130' and the frequency of reference signal 158 (see FIG. 1).
After the frequency offset is determined, frequency-mismatch can be
compensated, e.g., by applying to each digital sample a phase shift
equal to the frequency offset multiplied by 2.pi. and the time
elapsed between the start of the frame and the temporal position of
the digital sample.
At step 330 of method 300, additional signal processing is applied
to achieve channel estimation and compensation, and phase
estimation and compensation to recover the E-fields of the original
x- and y-polarization components, E.sub.x(t) and E.sub.y(t), as
assigned at transmitter 110. The channel-estimation/compensation
procedure of step 330 performs electronic estimation and
compensation of the phase and amplitude distortions imposed by
optical fiber transmission link 140, due to effects such as
chromatic dispersion, polarization rotation, and polarization-mode
dispersion. In one embodiment, the channel estimation relies on
digital samples corresponding to pilot symbols to determine the
channel-response function, H, of optical fiber transmission link
140. The inverse channel-response function H.sup.-1 is then applied
to the digital samples corresponding to payload data to perform
channel compensation. In another embodiment, the channel estimation
relies on blind adaptive equalization schemes such as constant
modulus algorithm (CMA), and modified version of CMA.
At step 340, phase estimation and phase compensation are also
performed, e.g., through the assistance of pilot symbols to correct
or compensate for slowly changing phase shifts between input signal
130' and reference signal 158 (FIG. 1). Various methods that can be
used for this purpose are disclosed, e.g., in U.S. Patent
Application Publication Nos. 2008/0152361 and 2008/0075472 and U.S.
Pat. No. 7,688,918, all of which are incorporated herein by
reference in their entirety. Blind phase estimation schemes such as
the Viterbi-Viterbi algorithm and the blind phase search algorithm
can also be used. In this manner the plurality of digital
electrical signals are processed to generate a set of values
representing 1-D modulated payload symbols.
At optional step 350, an inverse transform corresponding to a
unitary transform that generated the electronic representations of
the 1-D modulated signals is performed to obtain two
phase-conjugated 2-D modulated signals, E2D and E2D*. In one
embodiment, the inverse transformation has a generic form of
.times. ##EQU00014##
Then, coherent superposition of the two phase-conjugated 2-D
signals is performed to recover the original 2-D signal, E2D. In
one embodiment, the coherent superposition is performed as
E=[E2D+(E2D*)*]/2. (19)
At step 360, the recovered original optical signal field intended
for transmission, E(t), is renormalized, and either directly or
with reduced resolution fed into a soft-decision FEC, or
hard-decision FEC, to obtain payload data 102. In the case of
soft-decision FEC, an outer hard-decision FEC may be additional
used.
In various alternative embodiments of methods 200 and 300, the
order of certain processing steps may be changed to differ from the
order indicated in FIGS. 2 and 3, respectively.
FIG. 4 shows experimentally measured 15-Gbaud BPSK signal
constellations in the back-to-back configuration (left), after
6,400 km (80.times.80 km SSMF spans) with -2 dBm (middle) and 0 dBm
(right) signal launch powers, for the case without pre-dispersion
compensation (upper row, Dpre=0) and with the pre-dispersion
compensation according to the principles of the invention (lower
row, Dpre=-DL/2, where D=17 ps/nm/km and L=6,400 km). Clearly, the
performance obtained when the pre-dispersion compensation according
to the principles of the invention is applied is much better than
that obtained without pre-dispersion compensation. This outcome is
counterintuitive and non-obvious, as dispersion-compensation-free
transmission (including no pre-dispersion compensation) is commonly
preferred over dispersion-compensated transmission for obtaining
"better" nonlinear transmission performance. In addition, the
performances in the back-to-back configurations (without long-haul
fiber transmission) indicate that pre-dispersion compensation
actually results in a performance degradation, due to increased
digitization noise from the DACs (as pre-dispersion-compensated
signal has a higher peak-to-average-power ratio than the original
uncompensated signal). Moreover, the digital signal processing
(DSP) load needed to perform both pre-dispersion compensation at
the transmitter and post-dispersion compensation at the receiver is
usually much larger than that needed to perform post-dispersion
compensation only. Thus, performing the pre-dispersion compensation
for long-haul optical fiber transmission, especially for
dispersion-unmanaged optical links, appears to be not only more
burdensome in terms of implementation complexity, but also more
detrimental in terms of performance. Also, applicants have
confirmed that the performance improvement brought by the optimal
pre-dispersion compensation can only be obtained for optical
signals that are modulated according to 1-D modulation formats; for
instance a signal modulated according to a 2-D format will suffer
in performance with the application of the pre-dispersion
compensation.
FIG. 5 shows simulated 16-QAM signal constellations (left column)
without pre-dispersion compensation (upper row, Dpre=0) and with
pre-dispersion compensation (lower row, Dpre=-DL/2, where D=17
ps/nm/km and L=3,200 km), as compared to recovered 4-PAM signal
constellations (right column) without (upper row) and with (lower
row) pre-dispersion compensation. The results are based on
simulations with a link of 40.times.80 km SSMF spans and total mean
nonlinear phase shift of 0.5 rad. The results suggest that
intuitively, the "nonlinear distortion cancellation" effect due to
PCTW is transformed into the "nonlinear distortion squeezing"
effect for a pair of 1-D signals (which can be obtained by applying
a certain unitary transformation on the PCTW).
Various modifications of the described embodiments, as well as
other embodiments of the invention, which are apparent to persons
skilled in the art to which the invention pertains are deemed to
lie within the principle and scope of the invention as expressed in
the following claims.
Unless explicitly stated otherwise, each numerical value and range
should be interpreted as being approximate as if the word "about"
or "approximately" preceded the value of the value or range.
It will be further understood that various changes in the details,
materials, and arrangements of the parts which have been described
and illustrated in order to explain the nature of this invention
may be made by those skilled in the art without departing from the
scope of the invention as expressed in the following claims.
The use of figure numbers and/or figure reference labels in the
claims is intended to identify one or more possible embodiments of
the claimed subject matter in order to facilitate the
interpretation of the claims. Such use is not to be construed as
necessarily limiting the scope of those claims to the embodiments
shown in the corresponding figures.
Although the elements in the following method claims, if any, are
recited in a particular sequence with corresponding labeling,
unless the claim recitations otherwise imply a particular sequence
for implementing some or all of those elements, those elements are
not necessarily intended to be limited to being implemented in that
particular sequence.
Reference herein to "one embodiment" or "an embodiment" means that
a particular feature, structure, or characteristic described in
connection with the embodiment can be included in at least one
embodiment of the invention. The appearances of the phrase "in one
embodiment" in various places in the specification are not
necessarily all referring to the same embodiment, nor are separate
or alternative embodiments necessarily mutually exclusive of other
embodiments. The same applies to the term "implementation."
Also for purposes of this description, the terms "couple,"
"coupling," "coupled," "connect," "connecting," or "connected"
refer to any manner known in the art or later developed in which
energy is allowed to be transferred between two or more elements,
and the interposition of one or more additional elements is
contemplated, although not required. Conversely, the terms
"directly coupled," "directly connected," etc., imply the absence
of such additional elements.
The present inventions may be embodied in other specific apparatus
and/or methods. The described embodiments are to be considered in
all respects as only illustrative and not restrictive. In
particular, the scope of the invention is indicated by the appended
claims rather than by the description and figures herein. All
changes that come within the meaning and range of equivalency of
the claims are to be embraced within their scope.
A person of ordinary skill in the art would readily recognize that
steps of various above-described methods can be performed by
programmed computers. Herein, some embodiments are intended to
cover program storage devices, e.g., digital data storage media,
which are machine or computer readable and encode
machine-executable or computer-executable programs of instructions
where said instructions perform some or all of the steps of methods
described herein. The program storage devices may be, e.g., digital
memories, magnetic storage media such as a magnetic disks or tapes,
hard drives, or optically readable digital data storage media. The
embodiments are also intended to cover computers programmed to
perform said steps of methods described herein.
The description and drawings merely illustrate the principles of
the invention. It will thus be appreciated that those of ordinary
skill in the art will be able to devise various arrangements that,
although not explicitly described or shown herein, embody the
principles of the invention and are included within its spirit and
scope. Furthermore, all examples recited herein are principally
intended expressly to be only for pedagogical purposes to aid the
reader in understanding the principles of the invention and the
concepts contributed by the inventor(s) to furthering the art, and
are to be construed as being without limitation to such
specifically recited examples and conditions. Moreover, all
statements herein reciting principles, aspects, and embodiments of
the invention, as well as specific examples thereof, are intended
to encompass equivalents thereof.
The functions of the various elements shown in the figures,
including any functional blocks labeled as "processors," may be
provided through the use of dedicated hardware as well as hardware
capable of executing software in association with appropriate
software. When provided by a processor, the functions may be
provided by a single dedicated processor, by a single shared
processor, or by a plurality of individual processors, some of
which may be shared. Moreover, explicit use of the term "processor"
or "controller" should not be construed to refer exclusively to
hardware capable of executing software, and may implicitly include,
without limitation, digital signal processor (DSP) hardware,
network processor, application specific integrated circuit (ASIC),
field programmable gate array (FPGA), read only memory (ROM) for
storing software, random access memory (RAM), and non volatile
storage. Other hardware, conventional and/or custom, may also be
included. Similarly, any switches shown in the figures are
conceptual only. Their function may be carried out through the
operation of program logic, through dedicated logic, through the
interaction of program control and dedicated logic, or even
manually, the particular technique being selectable by the
implementer as more specifically understood from the context.
It should be appreciated by those of ordinary skill in the art that
any block diagrams herein represent conceptual views of
illustrative circuitry embodying the principles of the invention.
Similarly, it will be appreciated that any flowcharts, flow
diagrams, state transition diagrams, pseudo code, and the like
represent various processes which may be substantially represented
in computer readable medium and so executed by a computer or
processor, whether or not such computer or processor is explicitly
shown.
Embodiments of the invention find application in optical
communication systems including for example, ultra-long-haul
terrestrial and submarine transmission and other optical fiber
transmission systems in which increased transmission distance is
desirable. Embodiments may also allow rate-adaptive transmission
with much improved performance at low net data rates, which may be
valuable in ultra-long-haul transmission applications, especially
when fibers of high nonlinear coefficients (such as LEAF and TWRS)
are used. Compared to conventional approaches to increase the
distance of optical fiber transmission, embodiments described
herein may result in reduced the complexity and cost (especially
the operation cost) of the fiber link, with small modifications at
the optical terminals.
* * * * *
References